The hyperbolic n-space as a graph in euclidean (6n-6)-space.
Wolfgang Henke, Wolfgang Nettekoven (1987)
Manuscripta mathematica
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Wolfgang Henke, Wolfgang Nettekoven (1987)
Manuscripta mathematica
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J. E. Valentine, S. G. Wayment (1972)
Colloquium Mathematicae
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Jan Dymara, Damian Osajda (2007)
Fundamenta Mathematicae
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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.
Sergei Buyalo, Viktor Schroeder (2015)
Analysis and Geometry in Metric Spaces
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We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
Domingo Pestana, José Rodríguez, José Sigarreta, María Villeta (2012)
Open Mathematics
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If X is a geodesic metric space and x 1; x 2; x 3 ∈ X, a geodesic triangle T = {x 1; x 2; x 3} is the union of the three geodesics [x 1 x 2], [x 2 x 3] and [x 3 x 1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity...
Yamashita, Shinji (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Marcin Mazur (2013)
Annales Polonici Mathematici
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We give necessary and sufficient conditions for topological hyperbolicity of a homeomorphism of a metric space, restricted to a given compact invariant set. These conditions are related to the existence of an appropriate finite covering of this set and a corresponding cone-hyperbolic graph-directed iterated function system.
J. Aramayona (2006)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez (2013)
Open Mathematics
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We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given....
Avalishvili, G., Gordeziani, D. (1999)
Bulletin of TICMI
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Michał Kisielewicz (1975)
Annales Polonici Mathematici
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P. Colli, José-Francisco Rodriques (1991)
Forum mathematicum
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Sudhanshu K. Ghoshal, Abha Ghoshal, M. Abu-Masood (1977)
Annales Polonici Mathematici
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Wu, Yaokun, Zhang, Chengpeng (2011)
The Electronic Journal of Combinatorics [electronic only]
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Gvazava, J., Kharibegashvili, S. (1997)
Memoirs on Differential Equations and Mathematical Physics
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